Energy conservation for weak solutions to two-phase magnetohydrodynamic flows

In this paper, we consider the energy conservation of weak solutions to the two-phase magnetohydrodynamic flows in a bounded domain. We establish the Shinbrot-type regularity condition to ensure the energy conservation for a weak solution, which extends/improves previous various energy conservation works on Navier-Stokes-Cahn-Hilliard equations and MHD equations.